The purpose of this project is to measure forces and moments from existing orthodontic appliances and to evaluate the force systems produced. New appliances and modifications of existing appliances will be designed and tested to optimize the force system. Both material properties and design parameters will be studied. Forces will be measured in uniplanar and three-dimensional activations; with rigid and sliding supports; over small and large deflections; and between two teeth or larger multiple tooth units. The methodology is a combined experimental and analytical approach. Beam theory capable of handling large deflections in three dimensions in simple wires, wires with helices, and composite beams has been developed which are capable of measuring forces and couples at an attachment in three dimensions. A stereometric system is used to fully define displacement geometries. The clinical appliances that will be studied are headgear, root springs, lingual arch, alignment, loop design and straight wires, and retraction springs. The relevant mechanical properties of the orthodontic wires (modulus of elasticity, yield strength, and per cent elongation) will be studied in tensional, bending, and torsional modes. This knowledge will be used to better predict the action of orthodontic appliances and to improve their design.